#' @export
#'
#' @rdname dpaircase
#'
#' @param shape shape of the gamma distribution used for the serial interval
#'
#' @param scale scale of the gamma distribution used for the serial interval
#'
#' @param rate an alternative way to specify the scale of the gamma distribution
#' used for the serial interval
#'
dtemporal <- function(x, shape, rate = 1, scale = 1/rate, pi, alpha = 0.001) {
pi <- check_one_proba(pi)
alpha <- check_one_proba(alpha)
max_kappa <- get_max_kappa(pi, alpha)
weights <- get_weights(pi, max_kappa)
distributions <- convolve_gamma(shape, scale = scale,
kappa = max_kappa, keep_all = TRUE)(x)
out <- distributions %*% weights
return(as.vector(out))
}
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